I found 2 deep holes that look more like deep tunnels. The openings are not as large as the ones chipmunks make. Could these be voles? If so, how do I get rid of them before they start munching on roots?

You can trap a vole with a cage-style live trap, baited with apples and peanut butter. Place the trap alongside an active tunnel until you catch one. Move the vole as far away as possible before you release. An outside cat is also helpful at keeping voles from the garden. Check with your county extension agent for recommendations in your area.